# Lecture 21: NMR Spectroscopy I: 1H NMR

## Organic Chemistry I

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## Learning Objectives

By the end of this lecture, students will be able to:

1. Explain the physical basis of nuclear magnetic resonance spectroscopy
2. Predict the number of distinct 1H NMR signals from a molecular structure using symmetry analysis
3. Interpret chemical shift values to identify the electronic environment of protons
4. Apply the n+1 rule to predict splitting patterns
5. Use integration to determine the relative number of protons for each signal
6. Combine chemical shift, integration, and splitting to propose structural fragments

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## Lecture Content

### I. Physical Basis of NMR

Certain atomic nuclei possess a property called **nuclear spin**, characterized by a spin quantum number I. Both 1H and 13C have I = 1/2, making them NMR-active, while 12C and 16O have I = 0 and are NMR-inactive. In the absence of an external magnetic field, the spin states of a nucleus are degenerate (equal in energy). When the nucleus is placed in a strong external magnetic field (B0), however, the spin states split into two energy levels for I = 1/2 nuclei: the alpha state (aligned with the field, lower energy) and the beta state (opposed to the field, higher energy). The energy difference between these states depends on the strength of B0 and the gyromagnetic ratio of the nucleus.

**Resonance** occurs when radiofrequency radiation matching the Larmor frequency (the precession frequency of the nucleus in the magnetic field) is applied, causing nuclei to absorb energy and flip from the alpha to the beta state. Modern NMR spectrometers use **Fourier transform (FT) NMR**, in which a short radiofrequency pulse simultaneously excites all nuclei of a given type. The resulting free induction decay (FID) signal is mathematically transformed by Fourier analysis to produce the frequency-domain spectrum that chemists interpret.

### II. Chemical Shift

If all 1H nuclei resonated at exactly the same frequency, NMR would provide no structural information. Fortunately, the electrons surrounding each nucleus generate small local magnetic fields that slightly alter the effective field experienced by that nucleus, a phenomenon called **shielding**. More electron density around a proton produces greater shielding, causing it to resonate at a lower frequency. Less electron density results in deshielding and a higher resonance frequency.

**Chemical shift** (delta) expresses the resonance frequency of a nucleus relative to a reference standard in parts per million (ppm). The reference compound is **tetramethylsilane (TMS)**, Si(CH3)4, defined as 0 ppm. TMS protons are highly shielded because silicon is electropositive and donates electron density to the methyl groups. In the 1H NMR spectrum, signals appearing to the left (higher ppm) are described as downfield or deshielded, while those to the right (lower ppm) are upfield or shielded.

Several factors affect chemical shift. **Electronegativity** is the most direct: electronegative atoms such as O, N, F, and Cl withdraw electron density, deshielding nearby protons. The effect is cumulative and diminishes with distance. **Hybridization** matters as well: sp2 C-H bonds are more downfield than sp3 C-H bonds, with alkyl C-H appearing at 0.8-1.7 ppm, vinyl C-H at 4.5-6.5 ppm, and aromatic C-H at 6.5-8.5 ppm. **Magnetic anisotropy** from the circulation of pi electrons in double bonds and aromatic rings creates local magnetic fields that strongly deshield nearby protons, explaining why aromatic protons appear at 6.5-8.5 ppm and aldehyde C-H protons at 9-10 ppm. **Hydrogen bonding** causes O-H and N-H chemical shifts to be variable and concentration-dependent, ranging from 1-5 ppm for alcohols to 6-12 ppm for carboxylic acids.

<image>Panel A: A chemical shift correlation chart for 1H NMR. A horizontal axis from 0 to 12 ppm (TMS at 0). Colored bars indicate the typical chemical shift ranges for: alkyl C-H (0.8-1.7), allylic C-H (~1.7), C-H alpha to C=O (~2.0-2.5), C-H alpha to N (~2.2-2.9), C-H alpha to O (~3.3-4.0), vinyl C-H (4.5-6.5), aromatic C-H (6.5-8.5), aldehyde C-H (9.0-10.0), carboxylic acid O-H (10-12). Panel B: A diagram illustrating aromatic ring current anisotropy -- the aromatic ring is shown with circulating pi electrons generating a magnetic field; arrows show that protons in the plane of the ring (outside the ring) experience an augmented field (deshielded), while protons above or below the ring center would experience a diminished field (shielded). A caption reads: "Chemical shift values reflect the electronic environment of protons and are diagnostic for identifying functional groups."</image>

### III. Equivalent and Nonequivalent Protons

**Equivalent protons** are those in identical electronic environments, and they produce a single NMR signal. The number of distinct signals in a 1H NMR spectrum equals the number of unique proton environments in the molecule. Symmetry analysis is the key tool for identifying equivalent protons: if two protons can be interconverted by a symmetry operation such as rotation or reflection through a mirror plane, they are equivalent.

The **substitution test** provides a more rigorous approach. Mentally replacing each hydrogen with deuterium (D), if the resulting molecules are identical, the protons are equivalent. If the resulting molecules are constitutional isomers, the protons are nonequivalent. If they are enantiomers, the protons are enantiotopic and appear equivalent in achiral solvents. If they are diastereomers, the protons are diastereotopic and are nonequivalent.

Examples illustrate these principles. Ethane has all six hydrogens equivalent (one signal). Propane has two sets: six equivalent CH3 protons and two equivalent CH2 protons (two signals). Ortho-xylene (1,2-dimethylbenzene) has three sets of aromatic hydrogens and one set of methyl hydrogens.

### IV. Integration

The **area under each NMR signal** is proportional to the number of protons producing that signal. Integration does not provide absolute numbers but rather ratios. An integration ratio of 3:2:1 could correspond to 3H:2H:1H, or 6H:4H:2H, or any other multiple of that ratio. The molecular formula must be consulted to determine absolute proton counts. Modern spectrometers display integration either as a stepped line superimposed on the spectrum or as numerical values. Integration is indispensable for distinguishing between structural possibilities that would otherwise have similar chemical shifts.

### V. Spin-Spin Splitting (Coupling)

NMR signals often appear as multiple lines rather than single peaks, a phenomenon called **spin-spin splitting** or **coupling**. This arises because the magnetic field experienced by one proton is slightly modified by the spin states of neighboring protons on adjacent carbons, transmitted through the intervening bonding electrons.

The **n+1 rule** predicts the splitting pattern: a proton with n equivalent neighboring protons on adjacent carbons is split into n+1 lines. Zero neighbors produce a singlet, one neighbor a doublet, two neighbors a triplet, three neighbors a quartet, and so on. The relative intensities of the lines follow Pascal's triangle (1; 1:1; 1:2:1; 1:3:3:1; 1:4:6:4:1).

The **coupling constant (J)**, measured in Hz, is the distance between adjacent lines in a multiplet. The same J value appears in both sets of coupled protons, reflecting the mutual nature of the coupling interaction. Typical three-bond (vicinal) coupling constants are 6-8 Hz for freely rotating sp3 systems. Crucially, J is independent of the magnetic field strength, unlike chemical shift measured in Hz. Equivalent protons do not split each other.

Coupling is typically observed between protons on adjacent carbons (three bonds apart, vicinal coupling). Protons on the same carbon (geminal, two bonds apart) can also couple if they are nonequivalent. Long-range coupling over four or more bonds is usually small or absent except in rigid systems such as allylic or aromatic frameworks.

<image>A figure illustrating spin-spin splitting patterns. Panel A: The 1H NMR spectrum of 1,1-dibromoethane (CHBr2-CH3), showing a quartet at ~5.9 ppm (1H, coupled to 3 neighboring H) and a doublet at ~2.0 ppm (3H, coupled to 1 neighboring H). The coupling constant J is marked as the distance between lines in both multiplets, showing that J is the same in both. Panel B: A splitting tree (stick diagram) showing how one proton coupled to three equivalent neighbors produces a quartet (1:3:3:1 intensity ratio), with each successive split drawn step by step. Panel C: Pascal's triangle with rows labeled singlet through septet, showing the intensity ratios for each splitting pattern. A caption reads: "The n+1 rule and Pascal's triangle predict the number and relative intensity of lines in a split NMR signal."</image>

### VI. Complex Splitting and Special Cases

When a proton has two sets of **nonequivalent neighbors** with different coupling constants, the splitting pattern becomes more complex. For instance, a proton coupled to two Ha protons (coupling constant J1) and one Hb proton (coupling constant J2) produces a doublet of triplets when J1 does not equal J2, or a quartet when the two coupling constants happen to be equal. A splitting tree diagram is the best tool for working out these more complex patterns.

The **roof effect** is observed when coupled multiplets have similar chemical shifts: the inner lines of each multiplet are enhanced while the outer lines are diminished, causing the multiplets to "lean" toward each other. **O-H and N-H protons** often appear as broad singlets because rapid exchange between molecules averages out the coupling to neighboring protons. Their chemical shifts are variable and concentration-dependent. The **D2O shake** test, in which a few drops of D2O are added to the NMR sample, causes exchangeable O-H and N-H protons to be replaced by deuterium, making their signals disappear and confirming the presence of exchangeable protons.

### VII. Systematic Interpretation of 1H NMR Spectra

A reliable step-by-step approach to 1H NMR interpretation begins by counting the number of signals to determine the number of distinct proton environments. Next, note the chemical shift of each signal to identify the likely functional group environment. Determine the integration ratio to find the relative number of hydrogens for each signal. Analyze the splitting pattern of each signal to determine the number of neighboring hydrogens. Determine coupling constants to identify which signals are coupled to each other. Finally, combine all of this information with the molecular formula and degree of unsaturation to propose a structure, and verify that the proposed structure correctly predicts every observed spectral feature. Cross-referencing with IR and MS data, when available, strengthens the analysis.

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